Calculating-machine.



E.- LEDER.

CALCULATING MACHINE. APPLICATION FILED JAN.18, 190s.

HEBT 1.

Patented Oct. 27, 1908.

WITNESSES E. LEDER. CALCULATING MACHINE.

T 93 IE R 7 2L EM C OH m nv .m a P 0:11 1:611 an .0 E:

INVENTOR .ZJWJZ'Zeder WITNESSES ILLEDER. CALCULATING MACHINE.

APPLICATION FILED JAN. 18, 1908.

Patented 001;. 27,- 1908.

ATTORNEYS ERNST LEDER, OF BERLTN, GERMANY.

CALCULATING-MACHINE Specification of Letters Patent.

Patented Oct. 27, 1908.

Application filed January 18, 1908. Serial No.411,380.

To all whom it may concern:

Be it known that I, ERNST LEDER, a'subject of the Emperor-of Germany, and aresident of Berlin, Germany, have invented a new and Im roved Calculating-Machine, of which the fol owing is a full, clear, and exact description.

This invention relates to calculating machines, and more particularly devices of this which ordinary arithmetical calculations can I be made rapidly and accurately by the em- .ployment of logarithmic principles.

A still further object of the invention is to provide a calculating machine by means of which numbers can be ascertained when the respective logarithms of the numbers are known, and which has-a logarithmic scale so sub-divided and graduated that the logarithms of numbers from zero to ten thousand, and numbers from zero to ten thousand corresponding to known logarithms, can be ascertained therewith.

The invention consists in the construction and combination of parts 'to be more fully described. hereinafter and particularly set forth in the claims.

Reference is to be had .to the accompanyingdrawings forminga part of this specification, in which similar characters of reference indicate corresponding-parts in all the views, and in which Figure 1 is a longitudinal section of the calculating machine on the line"1 1-of Fig.

2-; Fig. 2is a plan view of the machine showing apart of the cover broken away ;-Fig. 3 is an enlarged plan view of a detail of the mechanism; F-igfil is aplan View of :a portion of the logarithmic scale employed, showing parts broken away; Fig. :5 is an enlarged side elevation of a detail; Fig. 6 is a longitudinal section of a portion of the machine showing the crank by means of which it-can be manually operated; Fig. 7 is an enlarged side elevationof the detail shown in Fig. '3; and Fig.

,8 is a diagramfillustrating the construction of the logarithmic'scale.

planation of my invention, it should be understood that while the form of the machine as illustrated in the accompanying drawings is designed for use with the Briggsian system of logarithms, in which the base is the number 10, the details of construction and the ar rangement of certain of the parts, such as the scale, can be altered to adapt the machine to the. use of other systems of logarithms, that is, systems of logarithms having base values other than 10. In the following description and claims, the term logarithm as usedis intended to apply to the Briggsian system of logarithms, which is one of the most widelyused.

Certain calculations, which are diflicult.

and laborious to make when the ordinary rules of mathematics are applied, can-be performed with ease and rapidity by the employment' of logarithms. For example, the raising of a number to a power, or the extraction of any root of a number, are easily effected logarithmically, while they involve extended arithmetical calculations if carried out in that way. By means of my calculatingmachi-ne, such calculations are performed by means of logarithms and can be effected in' a very simple manner and with great rapidity. At the same time, the device obviates the necessity of logarithmic tables, as by means of it the logarithm of any number, and conversely, any number corresponding to a known logarithm, can be obtained mechanically. In connection with the machine, I employ a special form of logarithmic scale which is sub-divided into a number of sections .and'fthus permits of the employment of an exceptionally great length of scale.

. Each of the scale sections is in the form of .an arc ofa circle, and all of the-sections areso arranged on a scale-carrying band that each can be easily and quickly arranged inposition to permit the calculations to be carried out. The diagram shown in Fig. 8 illustrates the method-of laying out the logarithmic scale. Thereotangle a 1) cd is bisected by the line e f. With the center h on the line e f an arc is described, passing through the pointsn and b and intersecting the line 'eyat -a, It. The length of this are should be ess than that of a full circle described with the radius h k. In the type of logarithmic scale which I employ in the form of the device shown, the are a k b is'exactly equal in length teens-third of the circumference of a circle Before roceeding to a more detailed exdescribed with the radius hie, and consequently, the angle a h b equals 120. A further arc is described with the center on the line e f passing through the points (1, c, and intersecting the line e f at i. The distamce l: i is equal to a, b, and b c; that is, the radius of the are d 'i c is equal to the radius of the are a k b. The distance 7c 11, is divided into a hundred equal parts, is k, k 70 k 1: 1:, .k" k. A series of arcs having theeenters on the line 6 f, and intersecting-the line e f at the .points 7c, k, W, k k, and similar to the arcs a Is b and d 'L c is described. Each of these arcs equals in len h one-third of the circumference of a circ e ofsimilar radius.

- In the rac'tical form of the scale, the arcs are inscribed upona band 1 of flexible mate'- rial such as fabric or the like, and as is shown in Fig. 4. The scales2 formed by the arcs are designated successively, by indicating figures 3 arranged at one side of the band 1; these figures are 00,01, 02, 03, 04 99. Each of the scale arcs 2 is divided in a thousand parts, that is, has a thousand graduations 4 inscribed thereon. The scale arcs indicate logarithmically, the numbers between 1.000 and 10.000. That is to say, the indicating figures 00, 01, 02, 03 99 of the scale arcs represent the first two figures of the mantissae of the logan'thmscorresponding to the numbers from 1.000, (one) to 10.000, (ten) and as each of the arcs is divided into a thousand parts by graduations, the latter will run from 000 to 990 and will correspond to the last three figures of the mantissae of the logarithms of the numbers between 1.000 and 10.000. The latter, themselves, are inscribed upon the scale arcs at the graduations which indicate the logarithms corresponding respectively to these numbers from 1.000 to 10.000. For example, the logarithm of the number 3.757 is 0.57484; consequently, the number 3.7 57 is indicated on the scale designated by the figure 57, that is, the first two numbers of the mantissa .57484, and it is indicated at the four hundred and eighty-fourth graduation of the scale are 57, reading from left to "right, of the thousand graduations inscribed u )on the scale are. In the illustration of the ogarithmic scale employed, the scale arcs are not shown actually divided into a thousand parts but are provided with a smaller number of graduations, for the sake of convenience. Upon the scale band at the side of the'scale opposite to the indicating figures 3 are inscribed numbers 5, .one for each scale, which correspond approximately, to the first number in scribed upon the respective scale. It will be --.understood that the mantissae of the logarithms of numbers which differ only in their decimal points, are the same,'the characteristics alone changing. For example: The logarithm of 3.757 is 0.57484, and the logarithmof 375.7 is 2.57484. Consequently, while the scale arcs actually correspond to numbers from 1.000 to 10.000 they can be used for numbers from .0001 to 10.000 and b methods of approximation, for numbers a ove ten thousand. In general, theo eration of the scale maybe exem lified as fol ows If the logarithm of a num er n comprises a I) a 100 P 100,000 100 100,000'

The graduation for the number n is found upon that are which is desi nated at the side by the figure a, and at film I) graduation,

the log. n

counting from left to right of the thousand graduations of the are in question. For the sake of convenience I have chosen to emplo exactly one hundred scale ares, and to divide each of the latter into a thousand equal parts. This relationship is not an arbitrary one and can be varied to suit convenience or individual preference. I refer to employ this number of arcs and this method of subdivision, as it permits a ractical and efficient construction of the mac inc.

Referring more particularly to the drawings, 6 represents the base of the machine, which, near the opposite sides, carries'elon gated walls or supports 7. A casing 8 is mounted upon the base and has a to or cover 9. Near the ends, the supports 7 l iave .journaled therein shafts 10 and 11 which carry rollers 12 and 13 respectively. The roller 12 has twenty-five teeth 14, at each end, adapted to engage with openings 15 at the opposite edges of the scale-band 1, the latter being rolled upon the roller 13 and passing over the roller 12. A shaft 16 is carried by the support 7 intermediate of the shafts 10 and 1]., and has a roller 17 upon which a portion of the band 1 is rolled in the opposite direction to the rolling of the band upon the roller 13. The band 1 extends from the roller 12 to the roller 13 adjacent to the under side of the cover 9, and can be moved with respect to the cover by operating the rollers, as will appear more clearly hereinafter. A pinion 18 is rigidly mounted upon the shaft 11 near one end thereof, and is in mesh with a gear-wheel 19 revolubly carried by one of the supports 7. The pinion has ten teeth, while the gear wheel has sixty teeth. The latter, further, has an arm 20 adapted to engage a stop 21 carried by the casing. The arrangement is such, that when the roller 13 is in its initial position the arm engages the stop and prevents further rotation of the roller 13 in one direction.

A crank 22 is rigidly carried by the shaft 10 and extends through a suitable opening of the casing. The crank has a spindle 23 projecting laterally therefrom and carrying a revoluble handle 24 by means of which the crank can be manually operated. At the end, the handle has a plate 25 provided with the adjacent gear 72 through a part of a' revolution such that the drum 69 has been moved through one-tenth of a revolution. The drum 68 is slidable upon the shaft 67, and by means of a handle 75 can be moved longitudinally of the shaft to disengage it from the intermediate wheel 73. By means of the handle 75 the drum 68 when disengaged from the intermediate wheel 73 can be set into any desired position. The cover 76 of the counter has openings 77 through which the figures of the respective drumscan be read, one at a time. Between the openings for the drum 68 and the remaining openings is inscribed a decimal point 78.

At the side of the bracket 62 remote from the gear wheel 61 are revolubly carried pinions 79, each of which has twelve teeth, and

which are in mesh. The bracket 62 is slidably'carried upon the frame 63 and can be moved along a guideway 80 by means, of a knob 81, .to throw either the wheel 61 or the pinions 79 into mesh with the gear wheel 59 and the pinion 66. It will be understood that when the gear wheel 61 is in an operative position the revolutions of the shaft 10 are indicated by the counter, each revolution being addedto the revolutions already made.

. When thepinions 79 are in an operative position the action of the counter is reversed and each revolution of the shaft 10 is subtracted from the revolutions already indicated by the counter. The wheel 61 is held against casual movement when the shaft 10 is revolving to return the scale-band to its initial position, by a spring 82 mounted upon the frame 63 and engaging the wheel 61.

At each end of the slot 32 is a recess 32 which permits the appearance of the figures at the opposite sides respectively of the scale band. By the use hereafter, of the term to set a number, is meant the bringing into the slot of that scale upon which the number in question appears and the placing of the over the graduapointer with the sight 47 tion of the scale which corresponds tov the number. The operation of the calculating machine is set forth in the following examples. of the uses to which it can be put. In each of the examples the machine is started from its initial position, that is, a position such that the hand 44 indicates 0, that the pointer is arranged at the left in its starting .will lie above the position and that ciphers appear in the sight 0 enings 77 of the counters. A stop 39 on t e cover 9 permits the operator to arrange the pointer exactly in its initial position.

Example I: What is log 371.5?

. In accordance with the logarithmic rule it appears that the characteristic of the desired logarithm is 2. The number 371.5 is set and when this has been done the sight and pointer graduation indicating the number 371.5. The scale are upon which the number 371.5 appears is characterized by the figure 56 which appears in the recess 32 at the left of the slot 32. In turning the scale band from its initial position to a position such that the scale are 56 appears, the shaft 10 has actuated the counter so that the figure 56 also appears to the right-'of the decimal point 78 in the corresponding sight opening 77. The number 56 represents the first two figures of the mantissa of the desired logarithm. -The oint 50 of thepointer 39 indicates the nine undred and ninetysixth graduation on the scale 53. The last number corresponds to the last three figures of the mantissa of the logarithm. Conse uently, the log 371.5 is 2.56996. It wil be understood that as the scale 53 in the form of the machine shown in the draw ings is divided into a hundred, points only, the last figure of the mantissa is approximated.

then appears at the counter. The pointer is set with-the sight at the graduation 1.04 of the scale are characterized by 01. The point 50 now indicates the graduation 703 on the scale 53.' In raising a number to a higher power by means of logarithms, the logarithm of the number is multiplied bythe power to which the number .is to be raised. Therefore, it is necessary to find the products of 01 X 10 and 703 X 10. These products are respectively 10 and 7030; the latter number represents seven scale arcs and thirty parts of the eighth, as each scale is divided into one thousand parts. Consequently, the first part of the mantissa is to be increased by 7; that is, to 17, while the last three figures of the mantissa are 030. set with the point 50 indicating 030 on the scale 53 and the crank is'turned until the number 0.17 appears at the counter, Thesight'of the pointer then indicates the graduation 14801 of the scale are characterized b 17, from which it appears that 1.04 1.4801.

Example IV: Z/175.02

The number 175.02 is set. The figures .24 appear at the counter. The pointer is arranged with the sight at the graduation 175.02 of the scale are characterized by 24. The point of the pointer then indicates the Example II: What is the number corre- The number 0.01

The polnter is then and projects the end of the pin 26 beyond the springs 33.

same andinto engagement with a plate 30 having a series of recesses 31 arranged in a circle concentric with the axis of the crank. The arrangement of these recesses is such that when the pin 26 engages one of the recesses a scale are is visible through a suitably formed slot or opening 32 in the cover of the machine. The shafts 11 and 16have coiled springs 33 connected therewithand rigidly secured to one of the supports 7. The coiled springs tend to rotate the shafts and to wind the scale band into an initial p0- sition, that is, the position such that the arm 20 engages the stop 21. If it is desired to set any particular scale in the slot 32, the

' handle 24 is pulled outwardly to free the pin 26 from the plate 30 and the crank is then turned until the desired scale are appears in the slot. The handle is then released and the pin engages one. of the recesses 31 of 'the plate to hold the band in position and prevent any movement of the rollers due to the The cover 9 of the machine casing has a circular opening 34 formed therein, in which is arranged a disk 35. The 0 enin-g 34 in cludes the slot 32, one side of w rich is formed by the edge of the disk 35 as is shown most clearly in Fig. 2. The edge of the disk is serrated or is provided with teeth 36. The disk is revolubly mounted upon a cross-member 37 of the machine casing by means of a pivot pin 38. A swinging arm or pointer 39 is pivotally mounted upon the pin 38 and extends across the disk 35 and the slot 32. Above the pointer, the pin 38 has a rigid pinion 40 having ten teeth. The pinion 40 is in mesh with a gear wheel 41 having a hundred teeth and rigid with a spindle 42 arranged to revolve upon a support 43 projecting from the cross-member 37. An indicating hand 44 is mounted upon the spindle 42 and extends over a graduated ring 45 mounted upon the crossanember 37. The ring 45 has inscribed thereon thirty graduations 46, running from 0 to 15 and O to]5.

The portion of the pointer 39 which extends over the slot is'forrned into a bifurcated frame 47 upon the sides of which is mounted a slidable crossbar 48 guided upon the sides by sockets 49. At the ends, the sides join to form a point 50. Between the sides of the part 47 of the pointer, and alined with the longitudinal center line of the pointer, is a sight 47 a by means of which the position of the pointer with respect to a scale are can be exactly determined. The

sight d7 is in alinernent with the point 50. The cross-bar sockets are serrated to engage at the periphery of the disk 35 and grip the same so that the disk is turned as the pointer is turned. A spring 51 secured to the crossbar and the pointer, holds the former nor mally in engagement with the disk. The frame 47 has a button 52 by means of which the pointer can be manually operated. By

moving the cross-bar against the tension of the spring, the sockets are released from the edge of the disk and the pointer can then be.

turned in one direction or the other without correspondingly actuating the disk. Concentric with the scale-arcslot 32, is a scale 53 inscribed upon the cover of the machine and having raduations from one to a thousand. In the rawings, the scale 53 is shown with only a hundred sub divisions, for reasons of simplicity, but in'the practical form of the device it is preferable to employ a scale with a thousand sub-divisions. y

The disk 35 has three e iii-distant indicating marks 54 thereon. T e marks extend to the periphery of the disk and are arranged -radially of the same, subtending angles. of

At one side, the shaft 10 extends through a suitable opening of the casing wall and has a rigid laterally rejecting arm 55 which car ries a pivoted 0g 56. A ratchet wheel 57 loose upon the shaft 10 and provided with twenty-five teeth is engaged by the dog 56. The latter is normally held in engagement with the ratchet wheel teeth by a spring 58. A Cgear wheel 59 having twenty-five teeth, an rigidly connected with the gear wheel 57 by means of a sleeve 60, is in mesh with a second gear wheel 61 also having twenty-five teeth. The gear wheel 61 is revolubly mounted upon a bracket 62 slidably arranged upon a frame 63 carried at the side of the casing. A counter 64 has a shaft 65 passing therethrough and carrying a pinion 66 provided with ten teeth and normally in mesh with the gear wheel 61. A second shaft 67 is arranged in the counter and has three drums 68, 69, and upon each of which are inscribed ten figures, from 0 to 9 inclusive. The drums 68, 69 and 70 are arranged in the order named from left to right.- The drum 70 is operatively engaged by a wheel 71 hav ing twenty teeth and rigid with the shaft 65. The drum 7O actuates the drum 69 through an intermediate gear 72. The drum 69 in turn actuates the drum 68 through an intermediate gear 73. The intermediate wheels 72 and 73 are nrounted upon a suitable shaft 72 carried by the counter frame. The arrangement is that of the ordinary counter and each of the drums 7 O and 69 has a pair of teeth 74 which engages the adjacent intermediate wheel once during each revolution of each drum. Therefore, when the drum 70 has completed one revolution it has turned oceans log vZ/i 75115 0.32044...

The crank is now turned until the number 0.32 appears atthe counter. The pointer is set. wit the sight indicating the graduation 044 of the scale 53. When the pointer has been arranged in this position the sight indicates the number 20914 on the scale are characterized by 32, andkirom this we find that 1 175.o2.=2.o914. Example V:

1779 o.19501 X28805 x0.00380 3 =52 The characteristics of the individual factors are in the order named 3, 1, 2, -3. The summation of these characteristics that is 3- 1 +23yields as result 1. By means of the handle 75 the counter drum 68 is set independently ot the other mechanism of the counter so that the figure 1 a pears in the sight opening of the counter at t e left of the decimal point.

The number 1779 is set and the ointer is positionedwith the sight indicating t e gradu ation 177 90f the scale are. The crank 1s then released to permit the scale are band to return to its initial position and thereupon the pointer is turned back into its original position, the cross-bar 48 being released so that the disk 35 is permitted to remain in the position to which it was brought when the pointer was swung from the'initial position to indicate the number 1779.

The number 19501 is set and the pointer positioned with'the sight indicating the graduation corres ondiin to 19501 oi the scale arc. The sea e are,- and is then allowed to return to its initial position and.the pointer is also returned to its initial position after being released from the disk. In the same manner the numbers 2885 and 3803 are successively set.

Each movement of the pointer from the .initial'position has rotated the disk to a certain extent. In setting the numbers suc- .cessively, the scale are hand was unwound and .a certain number 'of the scale arcs each of which corresponds to the first two figures .of a logarithm, was registered in the'counter.

The number 2.58 now appears at the counter.

"By means of the button 81 and the movable bracket 62, the pinions 79 are positioned bebetween the gear wheel 59 and the pinion 66 so that the operation of. the counter is reversed. That is, by means of the crank, the scale band is unwound from its initial osition and the counter is turned back unt' the number 2.00 appears instead of 2,538. One of the indicating marks 54 of the disk 35 will be found to register with one of the gradu'ations of the scale are characterized by 58, visible in the slot 32, and the graduation in question is found to be 38054. The figures 38054 constitute the resulting number, and as the characteristic 2 ap ears at the counter, the result of the calculation is 380.54.

As the disk is provided with equi-distant indicating marks 54, one of the same will always be found at that ortion oi the .disk which forms one side of t e scale arc slot 32. As the counter is actuated only when the scale band is being wound in one direction,

the counter will add up automatically the numbersof the scale arcs which are successively set in the slot 32. For instance, if the scale are band is first unwound from the initial position until the scale are characterized by 30 a pears, and then from its initial position until the scale are characterized by 60 appears, the counter. This means that the sum of the first two fi ures of the mantissae. of the logarithms in icated upon the respective arcs is .90, that is, .30 .60.

Example VI:

The characteristics of the numerator is 3.

the number .90 willappear at I The characteristic of the denominator it'actors are 0, 1, 0, and their sum'is therefore 1. Consequently, the characteristic of'the result is 2. By means of the handle 75 the counter is set so that the figure 2 appears at the left of the decimal point. The number 9751 is then set and the pointer positioned so that the si ht indicates the graduation 9751 of the sea e are. The scale are band is then permitted to return to its initial position and after releasing the pointer from the disk the pointer is turned back to its initial position. By means of the button 81 the counter is arranged so that its action is reversed; that is, instead of adding the successive movements of the scale are hand these are subtracted.

The number 8371 is then set and after releasing the pointer from the disk the pointer is moved from its initial position until it indicates the graduation 8371 of the scale are. In other words, the pointer is set at the regxuir'edgnumber without turning the disk.

s soon as the pointer is set it is permitted to clamp against the disk periphery and is returned to its initial position, consequently carr ing with itthe disk.

T e number 5055 is then set and the pointer positioned in the same way at the. raduation 5055 without rotating the disk.

, claim as new Patent counter.

pointer moved from the graduation 2701 to its initial position, carrying with it the disk.

The number 0.93 now appears at the An indicating mark 54 of the disk is found to correspond with a graduation 102 of the scale 53. The crank is then turned until the 0.00 appear at the counter, and it is then found that one of the indicating marks 54 of the disk corresponds with the number 8531 of the scale are appearin in the slot 32; As the figure 0 appears to the left of the decimal place in the counter the result of the calculation is 8.531.

The pinion 40 and the gear wheel 41 are so proportioned that every time the disk 35 ma res a complete revolution the hand moves one-tenth of the distance around the graduated ring 46, that is, it moves over three graduations. Thus we find that each graduation of the ring 46 corresponds to a third of a revolution of the disk 35, as the length of each scale are is equal to one-third of the circumference of the disk, that is, the peripheral distance between any two of the indlcating marks 54. Each time the disk makes a third of a revolution the hand will move from one graduation to the succeedgraduation on the ring 46.

n the examples given above, the factorsv and divisors were so chosen that the arcs, which, through the movement of the pointer and the disk are added, do not reach or exceed the length of a single arc. It often happens however, that the arc length is exceeded. When this occurs, the hand 44 indicates the total number of arc lengths through which the disk has been turned. For example, if during the course of a calculation the hand is positioned between +4 and +5 of the graduated ring, it appears'that the disk has been turned through four are lengths. In this case, the last figure ofthe number appearing at the counter must be increased by our.

It will be understood that I do not wish to limit myself in the form of my calculating machine to the exact constructive details illustrated in the accompanying drawings. If so desired, the proportions of the operatively connected parts may be altered or va ried and the method of operating the machine can also be changed. The underlying principles which I employ in this invention reside primarily in the form of the logarith mic scale, in the subdivision of the scale into a number of-sections which ermit the prac tical lengthening of the sea e, in the provi s1on of means for adding or subtracting the movements of the logarithmic scale-carrying member, and in the provision of means for adding or subtracting numbers indicated by thescale arcs themselves.

Having thus described my invention, I and desire to secure by Letters 1. In a calculating machine, a logarithmic scale comprising a plurality, of independent sections having successive graduations representing logarithmic values, and further having ndicated thereon numbers corresponding to the logarithmic values.

2. In a calculating mach-inc, a logarithmic scale comprising a plurality of independent sections each designated by a part 0 a logarithmic mantissa, and each having the remainder of the respective mantissae indicated thereon by a graduation.

3. In a calculating machine, a logarithmic scale comprising a plurality of independent sections designated successively by the first two figures of logarithmic mantissae, and each graduated to indicate figures of logarithmic mantissse other than the first two tigures.

4. In a calculating machine, a logarithmic scale comprising a plurality of independent sections designated successively by the first two figures of logarithmic mantissze, and each having graduations indicating the numbers from 000 to 999, said scale having indi cated thereon numbers corresponding to the logarithms represented by the section designations and graduations.

5. In a calculating machine, a logarithmic scale com rising independent sections each designated by the first two figures of a logarithmic mantissa, each of said, sections having one thousand graduations, whereby a number, the logarithm of which equals g -g6 is found on the 'section designated by 41:, and at the y-graduations of said a; section. 1

6. In a calculating machine, a logarithmic scale comprisin' independent sections designated by the t two figures of different logarithmic mantissre, each of'said sections having one thousand graduations, and further having indicated thereon numbers corresponding to logarithms, whereby a number,

if J

I I the logarithm of which equals 100 +100000 is indicated on the section designated by ac and at the graduation of said w-section designated by y.

7. In a calculating machine, a logarithmic scale comprising separate sections arranged in arcs of similar circles, and having the centers in alinement. v I

8. In a calculating machine, a logarithmic scale comprising independent sections formed in the arcs of circles having substantially equal'radii, the centers of said arcs being arranged in alinement, said arcs being designated respectively by parts of different logarithmic mantissee, said arcs further being graduated to indicate figures other than said parts of the respective logarithmic mantissae,

and having inscribed thereon numbers correspending to logarithms.

. termination of points thereon,

11. In a calculating machine, a movable logarithmicscale comprising separate sections designated successively by the first two figures of logarithmic mantissee, a fixed scale graduated to indicate figures of logarithmic mantissae other than the first two figures of the same, said fixed scale being adapted to cooperate with each of said sections to determine points on the same, said sections having indicated thereon numbers corresponding to the logarithmic values represented by the sections.

12. In a calculating machine, a movable logarithmic scale comprising separate. sections, said. sections being formed in the arcs of circles havingthe centers in alinement, means for operating said scale, means for concealing said scale, whereby one of said sections appears at a time, afixed scale concentric with said sections, and a. ointer extending over saidlogarithmic'sca e and said' fixed scale and arranged radially with respect to'said fixed scale and said logarithmic scale sections.

13. In a calculating machine, a movable logarithmic scale, means for actuating said scale, and a counter for registering the movements of said scale. I

14. In a calculating machine, a movable logarithmic scale comprising separate sections, means for actuating said scale, and a counter for re istering the sections through which said sca e is moved.

15. In a calculating machine a movable logarithmic scale comprising separatesections characterized successively by numbers beginning with 00 and increasing one unit for each section, means for concealing said scale-whereby but one of said sections appears at a time, means for actuating said scale, and a counter controlled by said actuating means and serving to re ister the sections successively appearing when said scale is actuated.

16. In a calculating machine, a movable logarithmic scale comprising separate sections characterized successively by numbers representing the first two figures of logarithmic mantissae, means for concealing said scale whereby but on. of sa1d sections appears at a time, means for actuating sa1d scale, means for returning said scale to an initial position, and a counter controlled by said actuating means and serving for the addition of the corresponding numbers of sections successively appearing when said scale Q 17. In a calculating machine,'a movable,

is actuated.

logarithmic scale comprising separate secji,

tions characterized successively by numbers representing the first two figures of log rithmic mantissae, means for concealing said scale whereby hpt, one of sa1d sect1ons ap.

pears at a time, means for actuating said scale, a counter controlled by sa1d actuating means and serving for the addition of the corresponding numbers of the sections sue-1 cessively appearing when said scale is actu f, ated, and means for reversing sa1d counter,

whereby sections successively appearing are successively subtracted by said counter. 18. In a calculatingmachine, a traveling band having a logarithmic scale thereon,

said scale comprising separate sections, means for actuating sa1d band, and a counter 'for registering the number of scale sections through which said band is moved.

19. In a calculating machine, drums, a

hand arranged upon said drums, whereiby in a plurality of positions, anda counter for registering the number of scale sections through which said band is moved.

20. In a calculating machine, drums, a

loo.

band arranged upon said drurns and having a,

prising separate sections, means;g;f r,jnea

mally resisting the displacement of said,

drums from an initial position, 1 neans for.

limiting the movement of IsaiddruinsLoIJe of the limits of movement of said drums? being" their initial position, means for actuating said drums, means for holding said band in a plurality of positions, means for concealing saidband whereby but one of said sections appears at a time, and a counter for registering the number of scale sections through which said band is moved.

21. In a calculating machine, a logarithmic scale, a movable member adapted to cooperate with said scale, and a movable pointer extending over said scale and controlli'n said member.

22. n a calculating machine, a movable logarithmic scale, a movable member adapted to cooperate with said scale, a movable pointer extendin over said scale and c011- trolling said mem er, and means for registering the movements of said member.

23. In a calculating machine, a logarithmic scale, a second scale, a movable member arithmic scale, and a pointer controlling said member and adapted to cooperate withboth of said scales.

24. In a calculating machine,a logarithmic scale, a second scale, a movable member having means for cooperating with said logarithmic scale, a pointer extending over said: scales and controlling said member, and means for registering the movements of said member.

25. In a calculating machine, a movable logarithmic scale, a fixed scale, a movable disk having means for cooperating with said logarithmic scale, a movable pointer extending over said scales and adapted to cooperate therewith, means for revolubly attaching said pointer to said disk, and means for registering the movements of said disk.

26. In a calculating machine, a movable logarithmic scale comprising separate successive sectlons formed in arcs of circles,

. means for concealingall but one of said sec,-

tions at a time, a fixed scale concentric with the visible one of said sections, a movable disk. concentric with the visible one of said sections, said disk having indicating means adapted to cooperate with said sections, a movable pointer extending over the visible one of said sections and said fixed scale and adapted to cooperate therewith, means for movably attaching said pointer to said disk whereby said disk can be caused to move with said pointer, and means for registering the movements of said disk.

27. In a calculating machine, in combiner tion, a movable logarithmic scale, means for registering the movements of said scale, a movable member adapted to cooperate with said scale, means for registering the movements of said member, and a ointer extend ber.

I 28. In a calculatlng machine, in combinaing over said. scale and contra g said memadapted to cooperate with said scale, means for addin and subtracting the movements of said mem er, a fixed scale, apointer extend- 1-ng over said scales and controlling said mem ber.

' I 29. In a calculating machine, in combination, a movable logarithmic scale, means for normally returning said scale to an initial 0- sition, means for holding said scale in a p rality of positions, means for adding and means for subtracting the successive movements of said scale, a fixed scale, a movable member ada ted to cooperate with said scale, means for adllingand means for subtracting the successive movements of said member, and a pointer controlling said member and adapted to cooperate with said scales.

30. In a calculating machine, in combination, a movable logarithmic scale comprising separate successive sections, each arrange in the arc of a circle, said sections being designated by the first two figures of logarithmic mantissae, said sections being graduated to indicate figures of logarithmic mantissae other than the first two figures, a fixed scale adapted to cooperate with said sections, means for actuating said logarithmic scale, means for adding and means for subtracting the successive movements of said logarithmic scale, a movable member adapted tocooperate with said logarithmic scale, means for adding and means for subtracting the successive movements of said member, means for limiting the movements of said logarithmic scale, and a ointer extending over said scales and having means for re movably attaching to said member whereby said member is controlled by said pointer.

In testimony whereof I have signed my name to this specification in the presence of two subscribing witnesses.

ERNST LEDER.

Witnesses WOLDEMAR HAUPT, HENRY HASPER. 

